What do coefficients in polynomial regression signify?

In polynomial regression, coefficients play a crucial role in defining the relationship between the independent variables and the dependent variable. More specifically, each coefficient associated with a term in the polynomial equation represents the degree of influence that the corresponding term has on the predicted value of the dependent variable.

When a coefficient is positive, it indicates a direct relationship; as the value of the independent variable increases, the predicted value also increases. Conversely, a negative coefficient implies an inverse relationship, where an increase in the independent variable is associated with a decrease in the predicted value. The magnitude of the coefficient indicates the strength of this relationship, with larger absolute values signifying a stronger impact.

Understanding these coefficients is essential for interpreting how well the polynomial model explains variability in the data and for making predictions based on changes in the independent variables. Therefore, they serve as crucial indicators of both the direction and strength of the relationships present in the model, confirming the correctness of the provided answer.